The function given in the image is:

$y = \frac{x^5 + 4x^2}{x^2}$

First, let's simplify the function:

$y = \frac{x^5}{x^2} + \frac{4x^2}{x^2}$

This simplifies to:

$y = x^{5-2} + 4x^{2-2} = x^3 + 4$

Now, let's find the derivative of $y$ with respect to $x$:

$\frac{dy}{dx} = \frac{d}{dx}\left(x^3 + 4\right)$

The derivative of $x^3$ is $3x^2$ and the derivative of the constant 4 is 0.

So, the derivative is:

$\frac{dy}{dx} = 3x^2$

Would you like more details on any specific step or have any other questions?

Here are some related questions you might find useful:

1. How do you find the derivative of a product of two functions?
2. What is the power rule in differentiation?
3. How do you apply the chain rule to find derivatives?
4. How do you find the second derivative of a function?
5. What is the significance of the derivative in calculus?

Tip: When simplifying a rational function before differentiation, always look for opportunities to cancel out terms to make the differentiation easier.